Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

Integrated Pipe Stress Analysis/Support Pattern Selection/Support Design CAE System

This paper describes the organization and features of the AUTO-PIPE CAE System. AUTO-PIPE is a fully integrated software package which allows the User to perform the entire sequence of piping analysis and design in a streamlined work flow process. Major tasks in this automatic process includes: (1) Pipe Stress Analysis (2) Pipe Support Location Optimization (3) Stress Isometric Drawing Generation (4) Pipe Support Pattern Selection and Member Design (5) 3D Interference Detection for Support At the core of the System is the AUTO-PIPE (Relational) Database which contains all static (project-specific) and dynamic (model-specific) data required for all of the major tasks listed above. The AUTO-PIPE CAE System has been used, and is currently being used, for pipe system design for Nuclear Power Plants in Japan to achieve substantial manpower reduction and cost savings.

Mechatronics at Rensselaer: Integration Through Design

Mechatronics is the synergistic combination of precision mechanical engineering, electronics, control engineering, and computer science in the design process. This paper describes a new elective course entitled Mechatronics which has been developed and was taught for the first time at Rensselaer during the fall 1991 semester to 45 senior-undergraduate and graduate students. The key areas of mechatronics which are studied in depth in this course are: control sensors and actuators, interfacing sensors and actuators to a microcomputer, discrete controller design, and real-time programming for control using the C programming language. The course is heavily laboratory-based with a two-hour laboratory weekly in addition to three hours of classroom lecture. The laboratory exercises include computer-aided control system design using MATRIXx, various analog and digital sensors, hydraulic actuators, DC and stepper motors, and computer control of a variety of physical systems. The unifying theme for the course is the integration of these key areas into a successful mechatronic design. Students are required, as a final project, to: identify a problem or need, analyze the problem, and write a problem statement; perform a state-of-the-art review; develop a list of specifications and identify the key specifications; generate an outstanding mechatronic-system conceptual design; and finally perform a detailed design of the system which may include model building and hardware development. Examples of student projects are described. This course should significantly enhance our design education program in the Mechanical Engineering Department and lay the foundation for the students to become mechatronic design engineers.

Implementation of p and h-p Versions of the Finite Element Method

Based on hierarchic shape functions and an effective convergence procedure, the p-version and h-p adaptive analysis capabilities were incorporated into a finite element software system, called COSMOS/M. The range of the polynomial orders can be varied from 1 to 10 for two dimensional linear elastic analysis. In the h-p adaptive analysis process, a refined mesh are first achieved via adaptive h-refinement. The p-refinement is then added on to the h-version designed mesh by uniformly increasing the degree of the polynomials. Some numerical results computed by COSMOS/M are presented to illustrate the performance of these p and h-p analysis capabilities.

A Domain Decomposition Study for a Parallel Finite Element Code

The primary objective of this study was the implementation and comparison of domain decomposition algorithms for a parallel Finite Element Method (FEM) used in the area of Computational Structural Mechanics (CSM). A parallelized FEM code exploits the concurrency inherent in the method to improve its computational efficiency. In order to use a larger size granularity in the parallel computation, the parallel FEM needs to partition its domain into subdomains in a proper manner. It is therefore necessary to search for domain decomposition algorithms to satisfy the special requirements of a parallel FEM. The domain decomposition algorithms investigated in this study physically decompose a meshed domain into a desired number of subdomains. Addressing the requirements of the parallel FEM, these algorithms are able to handle any type of two- and three-dimensional domains, balance the workloads across the multiple processors, minimize the communication overhead among the processors, maintain the integrity of each subdomain, minimize the overall bandwidth of the resulting system matrix, and require only a small amount of CPU time for the decomposition. Modifications to existing decomposition algorithms, such as the single wave propagating method and the bisecting method using vertical/horizontal cuts, are investigated. A new algorithm, based on the proposed multiple wave propagating method and the bisecting method using middle cuts, is formulated. These algorithms are compared with each other using performance criteria based on the overall FEM code and the algorithms themselves. An optimal combination algorithm is proposed. This algorithm combination is flexible and intelligent in some sense since several judgements are suggested to guide and organize different decompositions based on the general geometry of the meshes. The combination algorithm possesses both the desirable features of wave propagating and bisecting methods. As an application, the present algorithm is included in an existing parallel FEM code and some improvements in this code are made. The overall efficiency of the FEM code was increased.

Development of Finite Element Analysis Support System Based on the Hybrid Knowledge Model

This paper deals with conceptual orientation and system development of intelligent support system for general purpose FEA (finite element analysis) programs. An integrated support system called “InhierTalk” (Integrated interactive environment for hierarchical representation for FEA) has been developed in Smalltalk, an object oriented language, in order to confirm effectivity of hierarchical representation and to establish an optimum method of the system development. Two object-oriented knowledge models which consist of macro visual data representation and micro regularized data representation are proposed. In the development, it is found to be clear that active and passive evaluation methods are effective for construction of support system.

Penetration by Long Rods

This paper relates to the penetration of large, massive targets by long rods where target penetration is accompanied by rod erosion. A principal criticism of previous analyses of this problem by the present authors was the use of post test measurements to furnish input information for calculations. Thus, the analyses had no truly predictive capability. In particular, the profile hole diameter of the experimental target crater was previously employed as a measure of mushroom strain at the penetrator tip. Because this strain value has a significant effect on calculated penetration depths, it is very important to be able to predict it rather than measure it. In this paper a recent result from the analysis of the initial transient penetration phase is used to estimate mushroom strain. This result is incorporated into the previous steady-state analysis to make it predictive. This new theory is the basis for calculations that are compared with previously published experimental results. The degree of agreement is really quite good for a procedure in which there are no adjustable parameters. In any case, the new computational method is certainly a substantial improvement over the previous reliance on post impact information.

An Intelligent Mathematical Modelling Assistant for Analysis of Physical Systems

This paper describes work in progress aimed at developing an intelligent modelling assistant for the mathematical modelling task associated with engineering analysis. Mathematical modelling precedes detailed numerical analysis and involves formulating and evaluating engineering problems with the objective of proposing a candidate mathematical model that meets desired modelling requirements. The approach taken in this work is based on Chandrasekaran’s proposecritique-modify method which is adapted for modelling. The use of this paradigm is justified by viewing the mathematical modelling process as an activity of successive investigation and refinement of candidate mathematical models. The system architecture is based on exploiting a number of artificial intelligence techniques including model based reasoning, case based reasoning and rule based reasoning. A modelling options case base assists engineers in proposing candidate mathematical models. Engineering 1st principles and formulae are utilised within an artificial intelligence framework to provide a means of evaluating and critiquing the candidate mathematical models. The system is integrated with an existing interactive CAD system. The problem domain covered is application independent but will initially focus on the modelling and analysis of heat transfer problems.

An Interactive, Menu-Driven, Software for Flexural Analysis of Transversely Loaded Beams

A set of computer programs written in QuickBASIC language has been developed as an instructional aid for the Mechanics of Materials course. It consists of 9 programs and over 50 supporting subprograms. Starting with the span and loading inputs, this software computes the support reactions and displays the diagrams of distributed loads, shearing force, bending moments, slope, and deflection distributions. Disk files are created to save the input and computed data and also the resulting displays for quick retrieval during any phase of the flexural analysis. Various shapes of cursors are created on screen for the user to select any menu involved in the analysis and/or a desired section of the beam for computation of the principal and maximum shearing stresses, for which Mohr’s circle display is also an optional feature. All operations are interactive and menu-driven, and provided with many helpful prompting messages to assist the user to specify the next request.

Characterization of Modal Coupling in Nonclassically Damped Systems

A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. Clearly, the decoupling approximation is valid only if modal coupling can somehow be neglected. The purpose of this paper is to study the characteristics of modal coupling, which is amenable to a complex representation. An analytical formulation that facilitates the evaluation of modal coupling is developed. Contrary to widely accepted beliefs, it is shown that neither frequency separation of the natural modes nor strong diagonal dominance of the modal damping matrix would be sufficient to suppress the sometimes significant effect of modal coupling.